Beamforming techniques are used in conventional antenna systems and other communications devices. For certain applications, it is desirable to achieve a narrower beam (e.g., to allow devices to be smaller). Thus, there is a need in the art for improved receivers, transmitters, and other communications devices that can provide one or more narrow beams, for example to allow frequency re-use in a multi-user environment, and to improve gain against ambient noise by rejecting noise and interfering signals outside a given beam, among other advantages. The beam-width of an antenna or antenna array is normally limited by the diffraction pattern, which normally constrain arrays capable of generating or receiving narrow beams of radio-frequency (or acoustic) energy to be large as compared to the radiation wavelength. The techniques of Hermetic Transform beam-forming disclosed herein allow the diffraction pattern limits to be overcome.